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Genomes and Genes  basic reproduction numberSummarySummary: The expected number of new cases of an infection caused by an infected individual, in a population consisting of susceptible contacts only. Top Publications

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Publications
 Tanner M, Sattenspiel L, Ntaimo L. Finding optimal vaccination strategies under parameter uncertainty using stochastic programming. Math Biosci. 2008;215:14451 pubmed publisher..Results derived from a stochastic programming analysis can also help to guide decisions about how much effort and resources to focus on collecting data needed to provide better estimates of key parameters. ..
 Bacaer N, Ait Dads E. Genealogy with seasonality, the basic reproduction number, and the influenza pandemic. J Math Biol. 2011;62:74162 pubmed publisherThe basic reproduction number R (0) has been used in population biology, especially in epidemiology, for several decades. But a suitable definition in the case of models with periodic coefficients was given only in recent years...
 Rubel F, Brugger K, Hantel M, Chvala Mannsberger S, Bakonyi T, Weissenbock H, et al. Explaining Usutu virus dynamics in Austria: model development and calibration. Prev Vet Med. 2008;85:16686 pubmed publisher..Vet. Microbiol. 122, 237245]. These results suggest that the model presented is able to quantitatively describe the process of USUV dynamics. ..
 Bacaer N, Ouifki R. Growth rate and basic reproduction number for population models with a simple periodic factor. Math Biosci. 2007;210:64758 pubmed..population models with a periodic factor which is sinusoidal, both the growth rate and the basic reproduction number are shown to be the largest roots of simple equations involving continued fractions...
 Sun H, Lu X, Ruan S. Qualitative analysis of models with different treatment protocols to prevent antibiotic resistance. Math Biosci. 2010;227:5667 pubmed publisher..about the local or global stability of the equilibria of both models is carried out in term of the basic reproduction number R(0)...
 Hens N, Van Ranst M, Aerts M, Robesyn E, Van Damme P, Beutels P. Estimating the effective reproduction number for pandemic influenza from notification data made publicly available in real time: a multicountry analysis for influenza A/H1N1v 2009. Vaccine. 2011;29:896904 pubmed publisher..In this paper, we show how and in which situations the recorded history of cumulated case counts provides valuable information to estimate the effective reproductive number in an early phase and for a large number of countries. ..
 de Camino Beck T, Lewis M, van den Driessche P. A graphtheoretic method for the basic reproduction number in continuous time epidemiological models. J Math Biol. 2009;59:50316 pubmed publisherIn epidemiological models of infectious diseases the basic reproduction number 'R(0) is used as a threshold parameter to determine the threshold between disease extinction and outbreak...
 Nishiura H. Time variations in the generation time of an infectious disease: implications for sampling to appropriately quantify transmission potential. Math Biosci Eng. 2010;7:85169 pubmed publisher..an epidemic of Asian influenza A (H2N2) in the Netherlands in 1957 was reanalyzed, and estimates of the basic reproduction number, , from the LotkaEuler equation were examined...
 Diekmann O, Heesterbeek J, Roberts M. The construction of nextgeneration matrices for compartmental epidemic models. J R Soc Interface. 2010;7:87385 pubmed publisherThe basic reproduction number (0) is arguably the most important quantity in infectious disease epidemiology...
 Balcan D, Hu H, Goncalves B, Bajardi P, Poletto C, Ramasco J, et al. Seasonal transmission potential and activity peaks of the new influenza A(H1N1): a Monte Carlo likelihood analysis based on human mobility. BMC Med. 2009;7:45 pubmed publisher..We suggest that the planning of additional mitigation policies such as systematic antiviral treatments might be the key to delay the activity peak in order to restore the effectiveness of the vaccination programs. ..
 Coburn B, Wagner B, Blower S. Modeling influenza epidemics and pandemics: insights into the future of swine flu (H1N1). BMC Med. 2009;7:30 pubmed publisher..We discuss how the feasibility of controlling an epidemic critically depends on the value of the Basic Reproduction Number (R0). The R0 for novel influenza A (H1N1) has recently been estimated to be between 1.4 and 1.6...
 Korobeinikov A. Global properties of SIR and SEIR epidemic models with multiple parallel infectious stages. Bull Math Biol. 2009;71:7583 pubmed publisher..Depending on the value of the basic reproduction number R0, this state can be either endemic (R0>1), or infectionfree (R0< or =1).
 Hartemink N, Randolph S, Davis S, Heesterbeek J. The basic reproduction number for complex disease systems: defining R(0) for tickborne infections. Am Nat. 2008;171:74354 pubmed publisherCharacterizing the basic reproduction number, R(0), for many wildlife disease systems can seem a complex problem because several species are involved, because there are different epidemiological reactions to the infectious agent at ..
 Trapman P. Reproduction numbers for epidemics on networks using pair approximation. Math Biosci. 2007;210:46489 pubmed..Furthermore, in literature problems arise in defining basic quantities like the basic reproduction number R(0) and the realtime epidemic growth rate parameter r...
 Rebelo C, Margheri A, Bacaer N. Persistence in seasonally forced epidemiological models. J Math Biol. 2012;64:93349 pubmed publisher..In this paper we address the persistence of a class of seasonally forced epidemiological models. We use an abstract theorem about persistence by Fonda. Five different examples of application are given. ..
 Wesley C, Allen L. The basic reproduction number in epidemic models with periodic demographics. J Biol Dyn. 2009;3:11629 pubmed publisher..No general method exists for calculating the basic reproduction number, the threshold for disease extinction, in nonautonomous epidemic models...
 Vynnycky E, Edmunds W. Analyses of the 1957 (Asian) influenza pandemic in the United Kingdom and the impact of school closures. Epidemiol Infect. 2008;136:16679 pubmed..and clinical data from the United Kingdom from the 1957 (Asian) influenza pandemic, to estimate the basic reproduction number (R0), the proportion of infected individuals who experience clinical symptoms and the impact of school/..
 House T, Keeling M. Household structure and infectious disease transmission. Epidemiol Infect. 2009;137:65461 pubmed publisher..Since these benefits of childhood vaccination are a product of correlations between household size and number of dependent children in the household, our results are qualitatively robust for a variety of disease scenarios. ..
 Hosack G, Rossignol P, van den Driessche P. The control of vectorborne disease epidemics. J Theor Biol. 2008;255:1625 pubmed publisher..underpinning of our struggle with vectorborne disease, and still our strongest tool, remains the basic reproduction number, R(0), the measure of long term endemicity...
 Gran J, Wasmuth L, Amundsen E, Lindqvist B, Aalen O. Growth rates in epidemic models: application to a model for HIV/AIDS progression. Stat Med. 2008;27:481734 pubmed publisher..common quantity used to describe the growth of an epidemic when modelling infectious diseases is the basic reproduction number R0...
 Kamgang J, Sallet G. Computation of threshold conditions for epidemiological models and global stability of the diseasefree equilibrium (DFE). Math Biosci. 2008;213:112 pubmed publisher..sufficient condition for the global asymptotic stability of the DFE is R(0)< or =1, where R(0) is the basic reproduction number [O. Diekmann, J.A...
 Chowell G, Fuentes R, Olea A, Aguilera X, Nesse H, Hyman J. The basic reproduction number R0 and effectiveness of reactive interventions during dengue epidemics: the 2002 dengue outbreak in Easter Island, Chile. Math Biosci Eng. 2013;10:145574 pubmed publisher..reported prior to 2002 in Easter Island, the 2002 epidemic provided a unique opportunity to estimate the basic reproduction number R0 during the initial epidemic phase, prior to the start of control interventions. We estimated R0 at 27...
 Beretta E, Breda D. An SEIR epidemic model with constant latency time and infectious period. Math Biosci Eng. 2011;8:93152 pubmed publisher..e. the diseasefree equilibrium E0 and the positive equilibrium E+, which exists iff the basic reproduction number R0 is larger than one. If R0 > 1 we also provide a permanence result for the model solutions...
 Mwasa A, Tchuenche J. Mathematical analysis of a cholera model with public health interventions. Biosystems. 2011;105:190200 pubmed publisher..numbers R(E), R(V), R(T) respectively and the combined reproductive number R(C) are compared with the basic reproduction number R(0) to assess the possible community benefits of these control measures...
 Pellis L, Ferguson N, Fraser C. Epidemic growth rate and household reproduction number in communities of households, schools and workplaces. J Math Biol. 2011;63:691734 pubmed publisher..g. reproduction numbers, critical vaccination coverage, epidemic final size) to new results on the epidemic dynamics. ..
 Liu L, Zhao X, Zhou Y. A tuberculosis model with seasonality. Bull Math Biol. 2010;72:93152 pubmed publisher..Parameter values of the model are estimated according to demographic and epidemiological data in China. The simulation results are in good accordance with the seasonal variation of the reported cases of active TB in China. ..
 Bacaer N. Periodic matrix population models: growth rate, basic reproduction number, and entropy. Bull Math Biol. 2009;71:178192 pubmed publisher..Secondly, the formula for the basic reproduction number R0 in a constant environment is generalized to the case of a periodic environment...
 Stoddard S, Morrison A, Vazquez Prokopec G, Paz Soldan V, Kochel T, Kitron U, et al. The role of human movement in the transmission of vectorborne pathogens. PLoS Negl Trop Dis. 2009;3:e481 pubmed publisher..Understanding movement will facilitate identification of key individuals and sites in the transmission of pathogens such as dengue, which then may provide targets for surveillance, intervention, and improved disease prevention. ..
 Ma E, Fung C, Yip S, Wong C, Chuang S, Tsang T. Estimation of the basic reproduction number of enterovirus 71 and coxsackievirus A16 in hand, foot, and mouth disease outbreaks. Pediatr Infect Dis J. 2011;30:6759 pubmed publisher..This finding helps better understand the transmission dynamics of HFMD outbreaks and formulate public health measures for controlling the disease. ..
 Massad E, Coutinho F. Vectorial capacity, basic reproduction number, force of infection and all that: formal notation to complete and adjust their classical concepts and equations. Mem Inst Oswaldo Cruz. 2012;107:5647 pubmed..The analysis was intended to provide a formal notation that complete the classical equations proposed by these authors. ..
 Cross P, Johnson P, Lloyd Smith J, Getz W. Utility of R0 as a predictor of disease invasion in structured populations. J R Soc Interface. 2007;4:31524 pubmed
 Inaba H. On a new perspective of the basic reproduction number in heterogeneous environments. J Math Biol. 2012;65:30948 pubmed publisherAlthough its usefulness and possibility of the wellknown definition of the basic reproduction number R0 for structured populations by Diekmann, Heesterbeek and Metz (J Math Biol 28:365382, 1990) (the DHM definition) have been widely ..
 Goldstein E, Paur K, Fraser C, Kenah E, Wallinga J, Lipsitch M. Reproductive numbers, epidemic spread and control in a community of households. Math Biosci. 2009;221:1125 pubmed publisher..Along the way, we have also shown that in choosing between increasing vaccine efficacy and increasing coverage levels by the same factor, preference should go to efficacy. ..
 Zhang J, Jin Z, Sun G, Zhou T, Ruan S. Analysis of rabies in China: transmission dynamics and control. PLoS ONE. 2011;6:e20891 pubmed publisher..We estimate that the basic reproduction number R? = 2 for the rabies transmission in China and predict that the number of the human rabies is ..
 Chua T. Modelling the effect of temperature change on the extrinsic incubation period and reproductive number of Plasmodium falciparum in Malaysia. Trop Biomed. 2012;29:1218 pubmed..A temperature increase arising from the global climate change will likely affect the epidemiology of malaria in Malaysia, especially in the cooler areas. ..
 Spicknall I, Foxman B, Marrs C, Eisenberg J. A modeling framework for the evolution and spread of antibiotic resistance: literature review and model categorization. Am J Epidemiol. 2013;178:50820 pubmed publisher..Thus, even if all parameter values are correctly estimated, inferences may be incorrect because of the incorrect selection of model structure. Our framework provides insight into model selection. ..
 Hashmi S. La Gloria, Mexico: the possible origins and response of a worldwide H1N1 flu pandemic in 2009. Am J Disaster Med. 2013;8:5764 pubmed publisher..As a result of this study, we conclude that, with strict government measures to control the disease over an extended period of time, it is possible that many hundreds or even thousands of lives might be saved in the future. ..
 Chen Z, Zou L, Shen D, Zhang W, Ruan S. Mathematical modelling and control of schistosomiasis in Hubei Province, China. Acta Trop. 2010;115:11925 pubmed publisher..After analyzing the existence of the diseasefree equilibrium of the model, we determine the basic reproduction number and use the model to simulate the schistosomiasis infection data from Hubei Province...
 Edwards R, Kim S, van den Driessche P. A multigroup model for a heterosexually transmitted disease. Math Biosci. 2010;224:8794 pubmed publisher..These two cases are illustrated with parameters applicable to gonorrhea in the US. ..
 Ogunjimi B, Hens N, Goeyvaerts N, Aerts M, Van Damme P, Beutels P. Using empirical social contact data to model person to person infectious disease transmission: an illustration for varicella. Math Biosci. 2009;218:807 pubmed publisher..model estimation methods in how well they fitted seroprevalence data and produced estimates for the basic reproduction number R(0) and the effective vaccination level required for elimination of varicella...
 Bate A, Hilker F. Predatorprey oscillations can shift when diseases become endemic. J Theor Biol. 2013;316:18 pubmed publisher..These findings undermine any R(0) analysis based solely on steady states when predatorprey oscillations exist for density dependent diseases. ..
 Beggs C, Noakes C, Shepherd S, Kerr K, Sleigh P, Banfield K. The influence of nurse cohorting on hand hygiene effectiveness. Am J Infect Control. 2006;34:6216 pubmed..The study demonstrates that applying strict nurse cohorting in combination with good hygiene practice is likely to be a more effective method of reducing transmission of infection in hospitals. ..
 Inaba H. Endemic threshold results in an agedurationstructured population model for HIV infection. Math Biosci. 2006;201:1547 pubmed..Finally, we show sufficient conditions for the local stability of the endemic steady states. ..
 Lee J, Choi D, Cho G, Kim Y. The effect of public health interventions on the spread of influenza among cities. J Theor Biol. 2012;293:13142 pubmed publisher..First we obtain the basic reproduction number for the single city case, and observe two other control strategies suggested by this case: increasing ..
 Kenah E. Contact intervals, survival analysis of epidemic data, and estimation of R(0). Biostatistics. 2011;12:54866 pubmed publisher..Estimates of the contact interval distribution can be used to estimate R(0) in both massaction and networkbased models. We apply these methods to 2 data sets from the 2009 influenza A(H1N1) pandemic. ..